The Stacks Project.
The stacks project is an open source text book about algebraic stacks
and the algebraic geometry that is needed to define them. It is a resource
for algebraic geometers on foundational questions regarding schemes,
topologies on schemes, algebraic spaces, algebraic stacks, and more. It is
being written collaboratively and you can be part of it! Please visit its
main page.

Discussion of mathematical topics related to the stacks project and
regular updates can be found on my
Stacks Project Blog.

Here is a graph representing the logical implications in
the proof of the Cohen structure theorem for complete local rings.
The alphanumeric codes refer to tags in the project, explained in
the tags system.
Here are two different visualizations of the same result:
You can play around with these graps on the stacks project website.

Frobenius matrix computation project: see
Frobenius.
There is now an
executable
(compiled for generic x86 Linux machines)
that you can try. Brief instructions: Download the executable, and save it
as ``filename'' in a directory, change mode to executable, type
``./filename'' on the command line. Enjoy. Three versions:

Frobenius matrices of surfaces which are double covers of
weighted projective 2-spaces branched along curves:
executable

Feel free to email me with questions/comments/etc.

Preprints and papers

Here is a list of papers/projects with links to the .dvi-files
of some of the papers. Note that the .dvi files are not always
identical with the published version (but they are very close), as
in some cases editing was done after proof reading the proofs from
the journal in question.

A.J. de Jong, J. Starr, Every rationally connected variety
over the function field of a curve has a rational point,
American Journal of Mathematics, {\bf 125}, 567--580 (2003).
familyofcurves3.dvi
Here is the ad hoc argument showing how to obtain reduced fibres
after base change which was in theoriginal version of the preprint:
alternative.dvi

A.J. de Jong, The period-index problem for the Brauer group
of an algebraic surface, Duke Mathematical Journal, 123,
71--94 (2004). perind.dvi

A.J. de Jong, A result of Gabber,Preprint with
missing references about Br=Br' on quasiprojective schemes.
2-gabber.dvi or
2-gabber.pdf

J. Starr, A.J. de Jong, A remark on isotrivial families,
Preprint with missing references, precursor of the next entry.
JasonsTrick_final.pdf

J. Starr, A.J. de Jong, Almost proper GIT-stacks and discriminant
avoidance, Preprint with missing references and misleading title.
This paper also handles the period-index problem for Brauer groups
of surfaces over any algebraically closed field.
5-torsor.pdf

A.J. de Jong, Shioda cycles in families of surfaces,
Preprint on work in progress: Shioda.dvi

A.J. de Jong and N.M. Katz Counting the number of curves over a finite field. This unpublished note was written probably around the time I was in Princeton (1998-2000) since it resulted from discussions with Nick katz. It gives the trivial upper bound for the number of isomoprhism classes of genus g curves over F_q. Here is a link: curves.dvi.